A beam of electromagnetic (EM) radiation can be represented as a vectorial field that propagates along a given direction, which will be denoted by Z in this document. FIG. 1 is a schematic representation of a beam of light being focused by an optical system Σ in the region Ω. FIG. 1 shows a typical beam-like field E0(x,y,z) that propagates along the positive direction Z. A more explicit representation of the field would require a temporal variable, E0(x,y,z,t), that can indicate possible changes in time of the field; for example induced modulations by mechanical or opto-electronic means. The subject of this invention is applicable to time-varying electromagnetic fields as well. For simplicity, in the rest of the document, the possible temporal variation of the fields will be assumed as implicit, and the temporal variable will not be included in the text. If a beam of light propagates through an isotropic medium, its EM vector field, at every position within the beam, lies on a plane (X-Y) that is perpendicular to the direction of propagation. In other words, for a beam-like field there is no component of the EM field along the direction of propagation Z; or there is no longitudinal component of the EM field. In FIG. 1, E0(x,y,z) is the representation of an example of such a beam-like field.
When light is brought to a focus by an optical system (e.g. Σ at z=0 in FIG. 1, wherein Σ can be any optical system that focuses the beam, e.g. a combination of refracting and/or reflecting surfaces, a diffraction grating, etc.) with a sufficiently large numerical aperture (N.A.), the EM field (E1(x′,y′,z)) that is formed in the region Ω around the focus no longer necessarily lies on a single plane perpendicular to the direction of propagation of the original beam. Near the focal region Ω the general EM field possesses a longitudinal component, E1z(x′, y′, z), which is parallel to the direction of propagation of the original beam, as well as transverse components, E1x′(x′, y′, z) and E1y′(x′, y′, z), parallel to the plane X′-Y′. Note that the primed coordinates x′ and y′ are the same as x and y. The primed coordinate system around the focal region was chosen to emphasize the difference between the beam-like field and the focused field. The total longitudinal component of the focused field depends on the state of polarisation of the original beam, or more accurately, on the distribution of the state of polarisation across a transverse section of the original beam; in FIG. 1, for example, the field distribution E0(x, y, z=0) at z=0. This became well known since the publication of a seminal paper in 1959 by Richards and Wolf where they analysed a focused field in an aplanatic system, and is also true as long as the N.A. is sufficiently large, even if the system is not aplanatic; for example in the presence of optical aberrations, or dielectric interfaces. The vectorial structure of the EM field in the focal region of a high N.A. focusing system has been studied for several years now; its most common intended applications reside in the areas of optical storage, microscopy and scanning optical microscopy, photonic force microscopy, lithography, laser microfabrication, particle guiding or trapping, and single molecule imaging. The influence of the spatial distribution of the state of polarisation of the beam before it is strongly focused on the focused EM field has also been explored vastly. Perhaps one of the most common distributions is that of cylindrical vector beams, which include radial polarisation and azimuthal polarisation, but infinite number of other possibilities exist. Different polarisation distributions can be attained by using, for example, discrete polarisation elements like a pixelated spatial light modulator, continuous polarisation devices like the newly reported space-variant waveplate, or by simple phase and amplitude masks. Cylindrical vector fields can produce spots of focused light smaller than what scalar diffraction theory predicts. Susanne Quabis et al. published a remarkably clear and intuitive article in 2000 where they report that it is possible to produce foci of light of area as small as 0.1λ2 (where λ is used to represent the wavelength of the focused beam) using annular pupil apertures and radial polarisation. Most of the efforts to tailor or engineer the distribution of the state of polarisation of a beam have been aimed to produce the smallest possible spot of light at the region of focus, and hence achieve what is commonly referred to as imaging beyond the diffraction limit. These schemes, referred to as sub-diffraction limit imaging methods, base their so-called “super-resolution” on detecting the intensity of all the light that has been scattered from a spot of light that is smaller to what scalar diffraction predicts. Important attempts have also been made to determine the three-dimensional orientation of single molecules.
Reference is made to the method reported in 2005 by Ellis and Dogariu in which they describe a near-field method for characterising the polarisation properties of electromagnetic fields for which the electric field vector at a point may fluctuate in three dimensions. In their publication they model and measure the superposition of three orthogonal laser light beams generated by three independent laser sources, which form a three-dimensional electromagnetic field at the point where they intersect. Ellis and Dogariu used 9 different configurations of a near-field detector that consisted of two opposing near-field sharp fibers placed in close proximity to the point of the intersection of the beams. The relevance of their work to the present invention is the experimental verification, although by means of a near-field method, that there exists important and retrievable information in a three-dimensional electromagnetic field, they call this retrieval of polarisation information: “three-dimensional optical polarimetry”.
The aforementioned describes the principles of how it is possible to engineer a three-dimensional electromagnetic field by means of focusing a beam of light with a chosen distribution of the state of polarisation across its waist, using an optical system with a sufficiently high N.A. If such an illuminating focused beam impinges on a sample to be observed, i.e. optically analysed, the electromagnetic field that results from the interaction of the illumination light and the sample will be, in general, a three-dimensional vector field.
Most of the current optical methods for storing and reading data, and for analysing materials and biological tissue are based on the illumination, detection, and processing of the optical signal at a plane that is an optical conjugate of the recorded medium or sample under observation. For this reason the information is limited by the size of the smallest spot of light on the sample that those methods can produce. The vast majority of the optical storage methods are based on the principle of the confocal microscope, which relies on the collection of all the energy scattered from a sample in one single detector. This does not provide any means to retrieve information of the interaction of the sample with the longitudinal component of the focused field.
There are other methods that not only detect the total intensity of the scattered field but they also analyse the state of polarisation at a plane that is a conjugate to the sample. Such is the case of the multiplexing method by Torok et al., where they suggest the use of a polarising beam-splitter to multiplex the signal encoded in the angular orientation of a step-like feature in an optical disk. By using polarisation they claim that it is possible to detect different orientations of the step-like feature. There is no account in the patent by Torok et al. of the influence of the longitudinal component of the scattered field on the pupil of the optical system.
Only two patents and one scientific publication have made use of a limited part of the information of the state of polarisation on the pupil plane to assess optical properties of the object under observation. In the patent by Zhan and Legger and the one by Gold et al. only homogeneous linearly polarised light is used, which means that the longitudinal component of the electric field is zero at the center of the focused spot (on the optical axis), and negligible at positions near the optical axis. Hence, the EM field used to illuminate the sample is not considered as a three-dimensional field. The patents by Zhan and Legger and by Gold et al. relate to an incomplete polarimetry method known as ellipsometry. Both inventions treat the illumination and scattered field as simply composed by a finite number of rays with different angles of incidence on the sample, and do not even acknowledge that the field formed on the focusing region depends on the distribution of the state of polarisation on the entrance pupil of the illumination arm.
One scientific paper has been published where the authors claim they can simulate the assessment of the effect of a sample on the longitudinal component of a focused field. The technique reported is called “Z-polarised confocal microscopy”. The biggest limitation of this technique is that it only attempts to measure the effect of the sample on the longitudinal component of the field and no strategy is mentioned as to how to measure the effect of the sample on the transverse components of the focused field.
It is an object of the present invention to provide a new method or strategy to optically inspect a sample which is capable to retrieve information that is not available to any of the current state of the art technologies. Such a method or strategy would open a new domain for information from a sample to be read and stored.
It is a further object of the present invention to provide a method to measure or estimate a three-dimensional electromagnetic field without the need of a near-field probe.